Importance of multiscale analysis in HARDI studies

Introduction and Background. High angular resolution distribution diffusion imaging (HARDI) implicitly captures information about the structure in which the diffusion process takes place. HARDI allows examination of relatively wide range of diffusion signal angular frequencies that, due to the complexity of both diffusion process and its milieu, may spread over multiple bands. In consequence, we opt for multiscale analysis, probing all frequencies, but also favouring those frequencies that are more in concordance with our specific aims, which are to deduce and sharpen fibre distributions. Inherent HARDI signal sphericity motivated us to take on the concepts of multiscale spherical wavelet analysis. Since the directions of maximal diffusion are unknown a priori, HARDI explores the space in uniform manner, and thus suffers from a certain amount of information redundancy. HARDI projections onto predefined bases, like spherical harmonics (SHs)[1-4] can reduce the signal complexity, but are often not fully adapted to the problem at hand (e.g., fibre orientation distribution (FOD) sparsity). Deconvolution methods for FOD estimation [5,6], probe the signal locally, allowing for sparse representation, but are highly susceptible to noise. Nonetheless, they work quite well even at low b-values. Recently, an elegant framework for HARDI multiscale, ridgelet analysis was derived [7], reducing the signal representation to as little as 10 basis functions. We propose to denoise and sharpen the orientation distribution function (ODF) directly [8]. The algorithm that we employ is based on the spherical version of “à trous” algorithm [9], using B3-spline scaling function (defined in Fourier space). Using Funk-Radon relation between ODF and HARDI signal, we define a framework to probe HARDI signal directly and obtain a sparse and sharp representation of angular content of diffusion. Herein, we would like to stress the importance of multiscale signal analysis (through illustrative examples), and to show applications to real data, with as little as 64 directions, and b-value of 1000 s/mm2. Methods. Image Acquisition. Physical phantoms, emulating two fibre bundles crossing at 45° and 90° [10] were acquired on a 1.5T Signa MR system (GE Healthcare, Milwaukee), TE/TR =130ms/4.5s,12.0s (45° and 90° phantom, respectively), BW=200KHz. FOV = 32cm, matrix size of 32x32), b = 2000s/mm2, 4000 uniformly distributed orientations SNRmin > 4. The first real dataset was acquired on the same scanner. Twice refocused DW-SS-SE-EPI (TE/TR=100.2ms/19s, BW=200KHz, FOV=24cm on a 128x128 matrix, TH=2mm, 60 axial slices) was employed to obtain T2-weighted (b=0) and HARDI (b=3000s/mm2, 200 directions) data of a healthy volunteer (publicly available HARDI database [11]). The second real data set was acquired on 3T Trio MR system (Siemens, Erlangen). Parallel imaging with GRAPPA factor of 2 (TE/TR=147ms/11,5s, BW=1680Hz/pixel, 96x96 matrix, resolution 2x2x2mm, 60 axial slices) was employed to obtain T2-weighted (b=0) and HARDI (b=1000s/mm2, 64 directions) data of a healthy volunteer. ODF wavelet analysis. In [8], we derived in detail our algorithm for ODF wavelet-based denoising and sharpening. The analysis is redundant, and the frequencies decrease dyadically with increasing scales. The scaling function is spherical B3-spline, and wavelets at each scale are defined as the difference of “lowpass” signal content at two successive scales. The final ODF decomposition amounts to: Ψ= Ψ J + Σω j (Ψ stands for ODF, Ψ J for its lowest frequency content and ω j for its high frequency details, i.e., wavelets at each frequency scale j; j = 0 to J, and J = 2 for the experiments herein). Typically,